Hmmm, I would take a different approach to this.
A fever is an immune response to something. It's an inflammatory response. In the case of a virus or bacteria, or other foreign invader to your body it's your immune system trying to protect you and kill off the virus or bacteria. For this reason, it's often best to let a fever run it's course, unless the fever response gets out of hand and dangerous. If you take fever reducers at the first sign of fever you are disabling your immune system and may even prolong your illness.
About 40 - 50 % or so of folks who suffer with anxiety have a documentable, treatable, identifiable, chemical imbalance in the brain. The remaining folks are diagnosed as having an unknown cause or just suspected or assumed to have a chemical imbalance. More recently, it was discovered that an imbalance of certain bacteria in the gut can cause a chemical imbalance in the brain which in turn causes anxiety symptoms. There is some information on this out there on the web, you can research it for yourself. If this is the case, there are things you can do to improve or cure the problem. Things like therapeutic levels of probiotics, diet changes, food allergies, etc...
I have no idea if this is the case with you, but it would seem to be a possiblity. If I were you I would consider the low grade fever a sign of something going on in your body. It's NOT normal to have low grade fevers and there is ALWAYS a reason. A natural doctor would be extremely helpful with these issues and questions.
Oh, by the way CFS (Chronic Fatigue Syndrome) is also believed to be caused by a virus. I suggest you look up Dr Mercola's website and do a search on CFS, even anxiety or whatever else interests you. His site is an excellent source of reliable and unbiased scientific information written in an easy to read and understand format.